One way I approach this is to not take people's word for it, based on what appears to be either their beliefs, or precedent, but to try it out and see if (in your case) it matters in a way that you care about.
Here's a simple example: A 5 point Likert scale, with a uniform distribution. 100 people per group, and we'll do a two sample t-test. I'll repeat this 10000 times when the null hypothesis is true (i.e. there is no difference).
> mean(sapply(1:1000, function(x) {
t.test(sample(1:5, 100, TRUE), sample(1:5, 100, TRUE))$p.value
} ) < 0.05)
[1] 0.0499
It appears that I get a significant value 4.99% of the time. Given that I expect a significant value 5% of the time, it does not appear that violating the assumptions of normality and interval measurement has had any effect on my results - at least in terms of type I errors. (There might be power issues, of course.)
If someone has a specific criticism, you can investigate and see if it's an issue.
Here's another example: Now I have 5 people in one group, and 100 in the other.
> mean(sapply(1:10000, function(x) { t.test(sample(1:5, 5, TRUE), sample(1:5, 100, TRUE))$p.value } ) < 0.05)
[1] 0.0733
Now I have a 7.3% type I error rate. This is probably enough to worry about.
What about 5 per group?
mean(sapply(1:10000, function(x) { t.test(sample(1:5, 5, TRUE), sample(1:5, 5, TRUE))$p.value } ) < 0.05)
Now a 4.5% signifance rate - indicates a slight loss of power, but I prefer that (a lot) over an inflated type I error rate.
Best Answer
From the moment you decided to use Likert scales, the issue of whether or not the data were actually from a normal distribution was decided (in the negative). It's pointless to test (and answer with chance of error) a question to which you already know the answer with certainty (a large enough sample would always lead to rejection by a suitable test, but you can tell it is the case with no data at all). Your data are not from a normal distribution normal; that was already certain.
[However, it's also not a useful question to answer; a better question to answer is not 'are the data from a normal distribution?' (are they ever?) but 'how much impact does it have on my inference?', a question not answered by hypothesis tests.]
That depends on the parametric test. Parametric doesn't necessarily imply "normal"; you may be able to make some other distributional assumption that will be consistent enough with your situation that you would be content with the impact of whatever deviation from assumptions you have.
Beware - nonparametric tests also have assumptions, and in some cases may be somewhat sensitive to them.
Many nonparametric tests assume continuous data, for example, and if you don't account for heavy discreteness you may get tests with quite different properties from their nominal ones. Some assume symmetry. In addition, suitability of particular tests may depend on the precise hypothesis you're interested in - you may need some additional assumptions (or perhaps a somewhat different nonparametric procedure) to get a test of your actual hypothesis.
For very small $n$, that's not necessarily useful advice, since you may have no useful significance levels available to you. At larger (but still small) $n$, in cases where the assumptions of a suitable nonparametric procedure are tenable, it sometimes makes sense to avoid making parametric assumptions to which your inferences may be sensitive (though there's sometimes the possibility of choosing different, less sensitive procedures).
Which citations? What did they actually say?
No. A single item intended as part of a Likert scale is at least ordinal. If you have constructed a Likert scale by adding a number of such questions you have already assumed it was interval - by assuming things like '5'+'2' = '4'+'3' (which must be the case if you're able to add the scores and treat every '7' as the same), every component item had to have been interval. If they're interval, their sum certainly is.
I don't see how "use a parametric test" follows from that.
You say very little about what kind of hypotheses you have (what are you trying to find out?); more might be said in those circumstances.